The world number 15 got the better of her 40th-ranked opponent 11-7 11-7 11-7 after a 34 minute contest at the National Squash Centre.
Joshana Chinappa, another Indian in the fray, lost to New Zealand's world number seven Joelle King 5-11 4-11 5-11.
Pallikal's next match is against eighth-ranked Jenny Duncalf, whom she has not beaten in three meetings.
Prior to entering the tournament, Pallikal, the first Indian to break into the top-10 of world rankings, trained for two weeks in Australia with five-time World Open winner Sarah Fitz-Gerald.
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